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source: branches/f4grobner/termlist.lisp@ 153

Last change on this file since 153 was 150, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22(in-package :grobner)
23
24;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
25;;
26;; Low-level polynomial arithmetic done on
27;; lists of terms
28;;
29;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
30
31(defmacro termlist-lt (p) `(car ,p))
32(defun termlist-lm (p) (term-monom (termlist-lt p)))
33(defun termlist-lc (p) (term-coeff (termlist-lt p)))
34
35(define-modify-macro scalar-mul (c) coeff-mul)
36
37(defun scalar-times-termlist (ring c p)
38 "Multiply scalar C by a polynomial P. This function works
39even if there are divisors of 0."
40 (mapcan
41 #'(lambda (term)
42 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
43 (unless (funcall (ring-zerop ring) c1)
44 (list (make-term (term-monom term) c1)))))
45 p))
46
47
48(defun term-mul (ring term1 term2)
49 "Returns (LIST TERM) wheter TERM is the product of the terms TERM1 TERM2,
50or NIL when the product is 0. This definition takes care of divisors of 0
51in the coefficient ring."
52 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
53 (unless (funcall (ring-zerop ring) c)
54 (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))
55
56(defun term-times-termlist (ring term f)
57 (declare (type ring ring))
58 (mapcan #'(lambda (term-f) (term-mul ring term term-f)) f))
59
60(defun termlist-times-term (ring f term)
61 (mapcan #'(lambda (term-f) (term-mul ring term-f term)) f))
62
63(defun monom-times-term (m term)
64 (make-term (monom-mul m (term-monom term)) (term-coeff term)))
65
66(defun monom-times-termlist (m f)
67 (cond
68 ((null f) nil)
69 (t
70 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
71
72(defun termlist-uminus (ring f)
73 (mapcar #'(lambda (x)
74 (make-term (term-monom x) (funcall (ring-uminus ring) (term-coeff x))))
75 f))
76
77(defun termlist-add (ring p q)
78 (declare (type list p q))
79 (do (r)
80 ((cond
81 ((endp p)
82 (setf r (revappend r q)) t)
83 ((endp q)
84 (setf r (revappend r p)) t)
85 (t
86 (multiple-value-bind
87 (lm-greater lm-equal)
88 (monomial-order (termlist-lm p) (termlist-lm q))
89 (cond
90 (lm-equal
91 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
92 (unless (funcall (ring-zerop ring) s) ;check for cancellation
93 (setf r (cons (make-term (termlist-lm p) s) r)))
94 (setf p (cdr p) q (cdr q))))
95 (lm-greater
96 (setf r (cons (car p) r)
97 p (cdr p)))
98 (t (setf r (cons (car q) r)
99 q (cdr q)))))
100 nil))
101 r)))
102
103(defun termlist-sub (ring p q)
104 (declare (type list p q))
105 (do (r)
106 ((cond
107 ((endp p)
108 (setf r (revappend r (termlist-uminus ring q)))
109 t)
110 ((endp q)
111 (setf r (revappend r p))
112 t)
113 (t
114 (multiple-value-bind
115 (mgreater mequal)
116 (monomial-order (termlist-lm p) (termlist-lm q))
117 (cond
118 (mequal
119 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
120 (unless (funcall (ring-zerop ring) s) ;check for cancellation
121 (setf r (cons (make-term (termlist-lm p) s) r)))
122 (setf p (cdr p) q (cdr q))))
123 (mgreater
124 (setf r (cons (car p) r)
125 p (cdr p)))
126 (t (setf r (cons (make-term (termlist-lm q) (funcall (ring-uminus ring) (termlist-lc q))) r)
127 q (cdr q)))))
128 nil))
129 r)))
130
131;; Multiplication of polynomials
132;; Non-destructive version
133(defun termlist-mul (ring p q)
134 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
135 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
136 ((endp (cdr p))
137 (term-times-termlist ring (car p) q))
138 ((endp (cdr q))
139 (termlist-times-term ring p (car q)))
140 (t
141 (let ((head (term-mul ring (termlist-lt p) (termlist-lt q)))
142 (tail (termlist-add ring (term-times-termlist ring (car p) (cdr q))
143 (termlist-mul ring (cdr p) q))))
144 (cond ((null head) tail)
145 ((null tail) head)
146 (t (nconc head tail)))))))
147
148(defun termlist-unit (ring dimension)
149 (declare (fixnum dimension))
150 (list (make-term (make-monom dimension :initial-element 0)
151 (funcall (ring-unit ring)))))
152
153(defun termlist-expt (ring poly n &aux (dim (monom-dimension (termlist-lm poly))))
154 (declare (type fixnum n dim))
155 (cond
156 ((minusp n) (error "termlist-expt: Negative exponent."))
157 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
158 (t
159 (do ((k 1 (ash k 1))
160 (q poly (termlist-mul ring q q)) ;keep squaring
161 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring p q) p)))
162 ((> k n) p)
163 (declare (fixnum k))))))
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